A mosquito net positioned over a 7 ft 4 ft bed has a height of 3 ft . A mosquito enters the net through a hole located at one of the bed's corners. It then flies to and settles at the upper corner of the net that is diagonally opposite. Determine the magnitude of the mosquito's displacement.

Step-by-step solution

Let the corner of the bed where the mosquito enters be the origin (0, 0, 0) . The dimensions of the mosquito net are length l = 7 ft , width w = 4 ft , and height h = 3 ft . The coordinates of the diagonally opposite upper corner of the net are (7, 4, 3) . The displacement vector of the mosquito from the origin to this corner is s = 7 i + 4 j + 3 k . The magnitude of the displacement is given by | s | = 7^2 + 4^2 + 3^2 . | s | = 49 + 16 + 9 = 74 ft .